function getStuff(num, onContents){
$.getJSON('http://whateverorigin.org/get?url=' + encodeURIComponent('http://catholic.com/api-radio/' + num) + '&callback=?', function(data){
   //call the oncontents callback instead of returning
   onContents(data.contents);
});
}

//when calling getstuff, pass a function that tells what to do with the contents
getStuff(6387, function(contents){
window.GlobalVar = contents;
});

var NewVar = window.GlobalVar;
alert(NewVar);

getStuff(6387, function(contents){
    // the following statement will assign the value of 'contents' to the global variable 'GlobalVar'
    window.GlobalVar = contents;
});

var NewVar = window.GlobalVar;
alert(NewVar);

function getStuff(num) {
    $http.jsonp('http://whateverorigin.org/get?url=' + encodeURIComponent('http://catholic.com/api-radio/' + num) + '&callback=JSON_CALLBACK')
        .success(function (contents) {
            $scope.shows = contents;
        });
};
getStuff(6387);

.success(function (response) {
    var result = angular.fromJson(response.contents);
    $scope.shows = result.shows;
});

<ul>
    <li ng-repeat="show in shows">{{ show.title }}</li>
</ul>